Concept Quizzes

Challenge Quizzes

Parallelograms and Trapezoids

In the parallelogram above, we drew a perpendicular line from one vertex to the opposite side, then cut that piece off of the parallelogram, and added it to the other side of the parallelogram to create a rectangle. Can the pieces of a parallelogram always be combined like this to create a rectangle?

A parallelogram is converted to a rectangle by cutting and rearranging pieces of the shape, as shown above. Given that the area of a rectangle is \(\text{(base)}\times\text{(height)},\) is the area of a parallelogram also \(\text{(base)}\times\text{(height)}?\)

Two identical trapezoids combined to form the parallelogram, so the area of the trapezoid is half of the area of the parallelogram. Given the base lengths of Base 1 and Base 2, what is the area of the trapezoid?